Question

You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $8 and hour and your sales job pays $119 per hour. You need to earn at least $323 each week to pays your bills. Write a system of inequalities that shows the various numbers of hours you can work each job

Answer 1

To write a system of inequalities for the given conditions, we define x and y as the hours worked at the housecleaning and sales jobs respectively. The system consists of x + y <= 40 and 8x + 119y >= 323, which represent the limitations on working hours and earning requirements.

Step-by-step explanation:

The question involves creating a system of inequalities based on the given work and pay conditions. Let's denote the number of hours worked at the housecleaning job as x and the number of hours worked at the sales job as y. The combined weekly hours should not exceed 40, which gives us our first inequality:

1. x + y ≤ 40

Each job has a different hourly rate, with housecleaning paying $8 per hour and the sales job paying $119 per hour. The second inequality comes from the need to earn at least $323 each week:

2. 8x + 119y ≥ 323

These two inequalities represent the system that will show the various numbers of hours you can work at each job to meet your weekly hour limit and earnings requirement.